1

Fundamentals of Radiotherapy

Dr Simon Thomas

Medical Physics

Addenbrooke’s Hospital.

Fundamentals of radiotherapy• Radiotherapy is the use of ionising radiation

to treat disease (nearly always cancer)

• Aim of radiotherapy is to destroy cancer

cells, whilst not causing unacceptable

damage to healthy tissue.

• Need to ensure that radiation is targeted to

the disease, giving as little dose as possible

to healthy tissue

Target volume (prostate) surrounded

by organs at risk (bladder, rectum,

femoral heads)

2

Choice of energy

0

2 0

4 0

6 0

8 0

10 0

12 0

0 5 10 1 5 20 2 5 30

d e p th in c m

pe

rce

nta

ge

de

pth

do

se

2 50 kV

4 M V

1 6M V

How to produce MV x-rays

• Need to accelerate an electron and fire it

into a target

• Efficiency of x-ray production increases

with electron energy

• Efficiency of x-ray production increases

with Z of target

How to accelerate electrons

• Direct potential (20kV to 2MV)

• Indirect methods needed at higher energies

– Linear accelerators

– Betatrons

– Microtrons

– etc.

• Linear accelerators are the standard equipment used in radiotherapy

linear accelerators

- + - + -

+ - + - +

Accelerating waveguides

• Microwaves of 3GHz (10cm) in tuned resonant cavities

• Accelerating waveguide made form a series of cavities

• Travelling wave or standing wave can be used

• Can accelerate electrons by approx 15 MeV per metre

Linear acceleratorMagnetron

Electron gun

Accelerating waveguideTarget+ Flattening filter

Ion chamber

Collimators

3

Back to the patient – what arrangement

of beams should we use?

Simplify – square tumour in square patient

Outline

Target

Treatment planning aims:

• Normalise 100% of dose to centre of target

• Dose in target 95%-107%

• Dose outside target as low as possible

Single 6MV Beam Calculate isodose distribution

Colour wash and Isodose lines Isodose lines

Hot spot = 178%

Field edge =

50% isodose

target coverage

75% to 130%!

Build up region 1 to 3cm Add an opposed field

4

Hot spot = 116%

Field edge =

50% isodose

Isodoses

“neck”

inwards

Widen beams by

12mm each side

to get 95% to

cover ROI

target coverage

now 95% to

104%!

Add two lateral beams

Four Field Brick

Hot spot =101%

Max dose outside

target = 61%

12mm margin;

95% isodose is now too large

Reduce field widths

to 7mm margin

3 Field Brick

~30% dose in

posterior region

40° wedges,

70% weighting

Max dose outside

Target Volume =

87%

Remove posterior beam and add lateral wedges

5

Superior / Inferior coverage

Field lengths ~15mm

margin round volume

due to “necking”

Field widths

~7mm margin

Coronal View – cubic volume

95%

Isodose7mm field margins

Sup/Inf

15mm field margins

Sup/Inf

Coronal View – cubic volume

95%

Isodose

Conformal Volumes

Conformal –MLCs

Coronal View – spherical volume

Different margins!

95% isodose

surrounds target

volume

Clinical applications – Prostate with MLCs

Different margins &

asymmetric fields

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MLCs and wedges

Open field. Collimator 0 60° wedged field. Collimator 90

Intensity Modulated

Radiotherapy (IMRT)

• modification of the intensity of radiation across the beam profile to match the tumour. And avoid critical structures.

• Can get more complex dose distributions in 3D than with simple shaped fields.

Types of IMRT• Multiple static fields (“step and

shoot”)

• Dynamic MLC (“Sliding window”) – similar, but radiation stays on whilst MLCs move. Faster, but more to go wrong.

• Rotational IMRT – gantry rotates continuously whilst beam on and MLC varies. Known as “Rapid Arc” or “VMAT” (volumetric modulated arc therapy)

• Tomotherapy – Rotational IMRT on non-standard linac, with CT-like gantry and helical delivery.

Types of IMRT• Multiple static fields (“step and

shoot”)

• Dynamic MLC (“Sliding window”) – similar, but radiation stays on whilst MLCs move. Faster, but more to go wrong.

• Rotational IMRT – gantry rotates continuously whilst beam on and MLC varies. Known as “Rapid Arc” or “VMAT” (volumetric modulated arc therapy)

• Tomotherapy – Rotational IMRT on non-standard linac, with CT-like gantry and helical delivery.

Helical Tomotherapy• Purpose-built, integrated

device for IMRT & IGRT (of which more later)

• Helical delivery

– Fast

– Potential for high level of modulation

• Designed for IMRT

– Low leakage/scatter

– No flattening filter => simple beam modelling

Tomotherapy –IMRT delivery

Spiral CT

Delivery Sinogram for Helical Tomotherapy

•Based on same idea as spiral CT

•50-300 rotations, treated as 51

projections per rotation.

•At each projection, choose how

long each of the 64 binary MLCs

is open for

Giving high dose to prostate, medium

dose to nodes, and sparing the rectum.

7

Dose calculation algorithms

• How do we calculate the dose distributions

in radiotherapy treatment plans?

• Lots of algorithms in clinical use, with a

trade-off between speed and accuracy.

• One that is widely used is the

convolution/superposition algorithm.

Dose deposition kernel (probability distribution from a single photon

interaction) can be derived from Monte Carlo (Stochastic) models.

The dominant interaction is Compton; also PP and PE).

5 cm50cm

Can store pre-calculated kernels, or can fit to mathematical

models: e.g.

Where A,a,B and b are functions of angle, tabulated for a number

of energies by Ahnesjo 1989.

The first term relates mainly to primary dose (short range), the

second mainly to scattered photons (long range).

2/)(),( reBeArhrbra

wθθ

θθθ −− +=

TERMA• Total Energy Released per unit Mass

• It measures the energy removed from the

primary beam. Similar to KERMA, but

TERMA includes the energy lost to scattered

photons. KERMA does not.

• Convolve the TERMA with the energy

deposition kernel, to get the dose.

Calculating TERMA• Need to know the attenuation coefficient µ for

each point in the patient.

• This will depend on– The energy of the radiation (so you need to know the

spectrum)

– The electron density at each point (which can be calculated from the CT values)

• Strictly also need the physical density (since TERMA proportional to µ/ρ) but generally can assume that tissue is scaled water.

• Allow for geometrical penumbra by convolving with one or more gaussians

Convolution

• 3D convolution is inherently an N6 problem

• Using FFT reduces it to an N3log(N) problem (about a million times faster for N=256)

• Primary radiation attenuation depends on electron density –TERMA changes

• Attenuation of electrons and scattered photons depends on electron density – “kernel scaling”

• The shape of the kernel now depends on the densities between theinteraction point and the dose calculation point. Therefore no longer a true convolution, so cannot be done in Fourier space.

• So no longer an N3 log(N) problem, but back to a N6 problem

• This would be impossible, without an algorithm to speed it up. The one most people use in called the “collapsed cone” algorithm

)()()( gFFTfFFTgfFFT ×=⊗

))()((1gFFTfFFTFFTgf ×=⊗ −

The collapsed cone algorithm• Divide space around a point

into a series of cones

• Approximate that all energy

released in the cone is

transported and deposited

along the axis

• Calculation time is of the

order of M N3 where M is

the number of cones

considered for each point.

8

Collapsed conesNot like this

More like this

Or this

Perhaps “furled umbrella”

would be a better name than “collapsed cone”

Gross Tumor Volume

Clinical Target Vol.

Planning Target Vol.

Geometric uncertainty

Clinical Target Volume

• The CTV is a tissue volume that contains a

demonstrable Gross Tumour Volume (GTV)

and/or subclinical malignant disease, which

has to be eliminated. This volume thus has

to be treated adequately in order to achieve

the aim of radical therapy. (ICRU62)

Planning Target Volume

• The PTV is a geometrical concept used for

treatment planning, and it is defined to

select appropriate beam sizes and beam

arrangements, to ensure that the prescribed

dose is actually delivered to the CTV.

Why do

we need a

CTV to

PTV

margin?• To ensure that

the dose

distribution

covers the

CTV after

organ motion

and errors.

You might

actually be doing

this

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Or this

Types of errors• Gross errors

– include incorrect anatomical site or patient orientation, incorrect field size, shape or orientation or incorrect isocentre position of 3 standard deviations or more of the random error.

• Systematic errors – occur in the same direction and are of a similar magnitude for each

fraction throughout the treatment course. They may arise due to target delineation error, a change in the target position, shape and size, phantom transfer errors or set up errors.

• Random errors – vary in direction and magnitude for each delivered treatment fraction.

They arise from varying, unpredictable changes in the patients position, internal anatomy or equipment between each delivered fraction.

Systematic errors

• Also known as “preparation errors”

• Errors that apply to all fractions in the

same direction - these cause a shift in the

cumulative dose distribution relative to

the CTV

• Unknown and different for each patient

(if known can be corrected for and

removed)

examples of systematic errors

• CT scan used for planning is a snapshot - it may be at one end or the other of the random errors - ∑setup and ∑motion

• difference between simulator isocentre and linac isocentre, laser accuracy, CT-MR registration etc. ∑transfer (made of ∑linac ∑laser

∑CT ∑CT-MR ∑film etc.)

• Doctors delineation errors ∑doctor

Combining errors

• Systematic errors can be combined in quadrature with other systematic errors

• (sum the squares of all the errors, then take the square root)

• STV = CTV + margin for systematic errors

Margin for systematic errors

• The probability distribution follows a

Gaussian in three dimensions

• – if you are on the 10% level on the 3D Gaussian

means you miss the CTV for all fractions on 10% of

patients. It can be shown (for a perfectly conformal

95% isodose round a sphere) that.

Σ×= 5.2ginMar

Gives 95% isodose surrounding 90% of the patients.

This is the CTV to STV margin.

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Random errors

• Also known as execution errors

• Error can be translation or rotation

Examples of random errors

• Set-up errors

– Set-up of skin marks relative to linac

moves

– Bony landmarks vary relative to skin

marks

• Motion errors

– Organ moves from day to day relative to

bony landmarks

Margin for random errors

• Assume that they follow a Gaussian with

parameter σ

• Calculate dose distribution over course of

radiotherapy allowing for error distribution

• Observe how much smaller the 95% isodose

is

• That’s your margin

Recipe for margin - random errors

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-3 -2 -1 0 1 2 3

Series1

σ

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

sigma/cm

marg

in/c

m

full formula

0.7 * sigma

( )( )ppginmar σσσβ −+×=

5.022

σ×≈ 7.0ginmar

β=1.64 for single beam,

slightly smaller for

multiple beams.

222

motionsetup σσσ +=

Overall recipe

( )( )ppginmar σσσβ −++Σ=

5.0225.2

σ7.05.2 +Σ≈ginmar

•Systematic errors are worse than random

errors

Practical process of radiotherapy

treatment planning.• CT scan (and possibly MRI and/or PET)

• Outline on the images to delineate the target volumes and organs at risk.

• Add appropriate margins for geometrical uncertainty.

• Decide on appropriate doses

• Choose appropriate arrangement of beams

– either: Forward Planning (choose arrangement of beams until you get what you want).

– or: Inverse Planning (specify what you want, and get the computer choose the beams to achieve it).

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Forward planningInverse planning

• IMRT is too complex to just choose arrangement

of beams manually until the plan “looks OK”

• Instead have software that optimises the plan to

produce the “best” treatment plan

• For this to work, you need to have some measure

of what makes a good plan; you need some

mathematical objective function that you can

minimise.

• These can be based on Dose (minimum, maximum

etc. to volume), or on Dose Volume Histograms

Dose Volume Histograms

Either:

• What volume receives

a particular dose

(differential DVH)

• What volume receives

at least a particular

dose (cumulative

DVH)

0.0

50.0

100.0

150.0

200.0

250.0

300.0

80 85 90 95 100 105 110 115

percentage dose

cc

standard

IMRT

The Ideal DVH

0

20

40

60

80

100

120

0 20 40 60 80 100 120

% dose

% v

olu

me

PTV

OAR

Use of DVH as prescription

•Examples for PTV

–At least 99% of the

volume >95% of

prescribed dose

–Less than 1% of the

volume to exceed

105%

–Median to be

between 99% and

101%

Use of DVH for organs at risk

5068Fem.Heads

5100

2581

5068Bladder

5100

1595

3088

5081

6068Rectum

Max

Vol (%)

Dose

(%)Organ

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Prescriptions for IMRT• Dose based:

– I want the PTV to get 60Gy

– I want the OAR to get less than 50Gy

• Dose volume based:

– I want no more than 5% of the PTV to be below 60Gy

– I want no more than 50% of the rectum to exceed 50Gy

• Planning system will use these objectives to form an

Objective Function (otherwise known as a cost

function)

Dose-based penalty

0

50

100

150

200

250

300

350

400

40 45 50 55 60 65 70 75 80

Dose to point in target

Pe

nalt

y

0

50

100

150

200

250

300

350

400

30 40 50 60 70

Dose to point in OAR

pe

nalt

y

Penalty increases with square

of difference.

OAR has no penalty for under

dosing.Penalty is small if you only just fail. That’s why people tend to cheat by telling planning system a lower limit than the one they really want.DVH objectives and constraints

• Target– At least X% of the target should

receive at least dose Y

• OAR (and some targets)– No more than X% of the volume

should receive more than dose Y

• Hard Constraint– If it does not achieve the

constraint, then do not allow the solution.

• Objective or soft constraint– Apply a penalty for failure,

increasing the more you fail

- penalty = w ∆2

– The larger w the harder the constraint

∆

∆

∆

Target

Optimise to reduce objective function

• Gradient based – (need to be able to take derivative of objective function with relative to weight of all the sub-beams). Relatively fast, but can potentially get trapped in local minima

• Stochastic (e.g. simulated annealing) – much slower, but less risk of local minima.

• In practice you need to keep modifying your objective function to produce a clinically acceptable plan – mathematically optimal is not always clinically optimal.

• Where PTV extend into build-up region, the use of the PTV for optimisation can introduce problems.

Fractionation in radiotherapy

• If radiation given as a course of small “fractions” of radiation, recovery occurs between fractions

• If normal tissue can recover more quickly than tumour, this improves the therapeutic ratio

• Most fractionation schemes are empirical, based on clinical experience

Linear Quadratic theory

• If dose Dx is given in fractions of dx , this is gives equivalent cell killing to a dose of D2 in 2 Gy fractions, where

• can also define a Biologically Equivalent Dose equal to dose in notional tiny fractions

� α/β is typically 10-20Gy for tumours, typically 2 Gy for later-responding side effects

)(survival) celltarget ln( 2dd βα +−=

( )Gy

dDD x

x2

)(2

+

+=

βα

βα

+=

βα

dDBED 1

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Fractionation in radiotherapy

• Delivering dose as a series of small fractions will reduce the difference between the two curves, and cause less harm to normal tissues for the same tumour kill

• Normal tissues have greater power to recover between fractions of radiotherapy than tumour has

• A course of radiotherapy is typically 50 to 74 Gy, given in 2Gy daily fractions (5 per week)

0.01

0.1

1

0 1 2 3 4

α/β 2

α/β 10

Image-guided Radiotherapy

• If you can image the patient every day in the treatment position, you can reduce the systematic and random errors. This should enable a smaller margin to be used, and hence reduce normal tissue damage.

• Image patient from exit beam.

• Can reconstruct CT-image

– Cone-beam using detector on conventional linac

– Dedicated “tomotherapy unit” based on CT gantry

IGRT

MV helical CT on

Tomotherapy unitkV cone-beam CT on Elekta

Synergy.

IGRT

IGRT

Brachytherapy

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What is Brachytherapy?

The placement of radiation sources in or near the patient. Three categories :-

1) Intra-cavity - sources placed inside natural body cavity. e.g. Ca cervix treated with uterine / vaginal sources.

2) Interstitial - sources surgically implanted in and around tumour. e.g. iridium in breasts. iodine seeds in prostate

3) Mould - the use of surface applicators to hold sources next to patients skin. e.g. skin tumours

Intracavitary Treatment (Cervix)

Interstitial (seeds implant to

prostate)Interstitial (Iridium to the tongue)

Ideal Source for Brachytherapy

1) γ-ray emitter. High enough energy to minimise scatter and avoid increased energy deposition in bone by PE. Low enough energy to minimise protection requirements. This gives the range 200 - 400 keV.

2) Half life. Long enough to minimise decay corrections during treatment. Too avoid frequently buying new sources, a very long half-life is desirable. For permanent implants, shorter half-lives are needed.

3) Charged particle emissions absent or easily screened.

4) No gaseous disintegration products.

5) High specific activity

6) Insoluble and non-toxic chemical form.

7) Does not powder/ disperse if casing

damaged.

8) Can be made into different sizes and shapes

(tubes, needles, spheres, flexible wires). If in

wire form must be able to be cut without

causing contamination.

9) Not damaged during sterilisation.

10) Cheap/ easily available (especially for

"disposable" sources).

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Sources - what is available:

Isotopes :-

• naturally occurring.

• reactor produced :- fission products.

• neutron activation (n,γ) products.

• Radium and Radon no longer used.

• Most commonly used isotopes are Ir-192 and I-125

• Cs-137, Co-60 and Pd-103 used in some applications

Commonly used gamma-emitting

Nuclides

17 days

0.02

(<0.1%)

Pd-103

74 days

0.3-0.6

(mean=

0.36)

1.9

Ir-192

59 days30 years5.3

years

Half life

0.030.661.17

and

1.33

Gamma-

ray

energy

(MeV)

(<0.1%) HVL=1.3cm

tissue

1219Transmission

through 2cm

Pb (%)

I-125Cs-137Co-60Nuclide

Isodose Plot

• If one evaluates dose over a grid of points and then

joins the points of equal dose, we get an isodose

plot (cf external beam treatment planning)

Isodose plots and dose-volume

histograms

Radiotherapy Physics. Summary• Most radiotherapy given with external beam x-

rays, mostly with linear accelerators.

• Multiple beams used to give good target coverage. Intensity modulated radiotherapy (IMRT) enables shaping of high dose regions in three dimensions.

• Fractionated doses given to improve therapeutic ratio.

• Geometrical uncertainties mean we need to add margins. Image Guided Radiotherapy has potential to reduce these margins.

• Brachytherapy puts sources inside the patient, to irradiate from within.